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Journals / Sakarya University Journal of Science / 2026 / Volume: 27 Issue: 1

Finitely-cosmall Quotients

Berke Kaleboğaz(Hacettepe Üniversitesi)0000-0002-4903-2244
Pages
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Publication Date
2023-02-28
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, we obtain an example of right minimal morphisms by using finitely-cosmall quotient (singly-cosmall quotient) morphisms.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we first define the notion of finitely-cosmall quotient (singly-cosmall quotient) morphisms.
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Key Findings & Data:Then we give a characterization of this new concept.
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Conclusion & Impact:Moreover, we obtain an example of right minimal morphisms by using finitely-cosmall quotient (singly-cosmall quotient) morphisms.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Pure-cosmall quotient morphisms · finitely-cosmall quotient morphisms · right minimal morphisms

Abstract

In this paper, we first define the notion of finitely-cosmall quotient (singly-cosmall quotient) morphisms. Then we give a characterization of this new concept. We show that an epimorphism p:Y→U is a finitely-cosmall quotient (singly-cosmall quotient) if and only if for any right R-module Z any morphism g:Z→Y such that pg is a finitely-copartial isomorphism (singly-copartial isomorphism) from Z to Y with codomain U is a finitely (singly) split epimorphism. We also investigate the relation between pure-cosmall quotient and finitely-cosmall quotient (singly-cosmall quotient) morphisms. We prove that over a right Noetherian ring R, an epimorphism p:Y→U is a pure-cosmall quotient morphism if and only if p is a finitely-cosmall quotient (singly-cosmall quotient) morphism. Moreover, we obtain an example of right minimal morphisms by using finitely-cosmall quotient (singly-cosmall quotient) morphisms.

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Cite This Article

Kaleboğaz, B. (2023). Finitely-cosmall Quotients. Sakarya University Journal of Science, Volume: 27 Issue: 1. https://doi.org/10.16984/saufenbilder.1158987

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